Aspects of the present disclosure can be embodied in a systems for heating an exterior surface of a bulk medium. In one example, the system includes two or more coupling strips spaced apart from one another and attached to the bulk medium. Each of the coupling strips has a multi-layer structure extending along a surface of the bulk medium that forms, in combination with the bulk medium, an electrical transmission line. The multi-layer structure includes a first dielectric layer over the bulk medium, a conductive layer over the first dielectric layer, a second dielectric layer over the conductive layer, and a conductive shielding layer over the second dielectric layer. A power control system is coupled to the conductive layer of each of the coupling strips and to the bulk medium. The power control system is configured to heat the bulk medium by providing current to the coupling strips.
Legal claims defining the scope of protection, as filed with the USPTO.
. A system for heating an exterior of an aircraft, the system comprising:
. The system of, wherein each of the coupling strips extend from a forward end of a wing towards an aft end of the wing.
. The system of, wherein the wing comprises at least one of a vertical stabilizer or a horizontal stabilizer.
. The system of, wherein the coupling strips are spaced apart along a direction from a base of the wing towards a tip of the wing.
. The system of, wherein the surface of the aircraft skin comprises at least one of an aircraft fuselage, a horizontal stabilizer, a vertical stabilizer, or an engine nacelle.
. The system of, wherein a width of each coupling strip is less than a spacing between coupling strips and a length of each coupling strip is greater than the spacing between coupling strips.
. The system of, wherein the conductive layer comprises copper, and wherein the aircraft skin comprises an electrically conductive material having an electrical resistance greater than that of copper.
. The system of, wherein the conductive layer comprises silver, and wherein the aircraft skin comprises an electrically conductive material having an electrical resistance greater than that of silver.
. The system of, wherein the conductive layer comprises aluminum, and wherein the aircraft skin comprises an electrically conductive material having an electrical resistance greater than that of aluminum.
. The system of, further comprising a power supply configured to provide electrical current to the coupling strips at an AC frequency between 1 kHz and 450 MHz,
. The system of, wherein the conductive layer of at least one of the coupling strips is folded one or more times such that segments of the conductive layer lie alongside one another.
. The system of, further comprising a power control system that is electrically connected to the conductive layer of each of the coupling strips at the input end and is electrically connected to the aircraft skin at the input end of each coupling strip, wherein the power control system is configured to provide AC electrical current to the coupling strips and to the aircraft skin.
. The system of, wherein, during operation, current at the termination of the conductive layer in each of the coupling strips is zero.
. The system of, wherein the power control system is coupled to a first one of the two or more coupling strips by a connector that includes impedance adjusting components within the connector.
. The system of, wherein the power control system is coupled to coupling strip connectors (CSC), each CSC comprising a first terminal connected to the conductive layer of a respective one of the coupling strips at the input end and a second terminal connected to the aircraft skin at the input end of the respective one of the coupling strips, and
. The system ofwherein the at least one CSC further comprises a reactive element connected.
. The system of, wherein the power control system is coupled to coupling strip connectors (CSC), each CSC comprising a first terminal connected to the conductive layer of a respective one of the coupling strips at the input end and a second terminal connected to the aircraft skin at the input end of the respective one of the coupling strips, and
. The system ofwherein the at least one CSC further comprises a reactive element.
. An aircraft comprising:
. The aircraft of, further comprising:
. The aircraft of, wherein the AC power control circuitry is configured to:
. The aircraft of, further comprising:
. The aircraft of, wherein the AC power control circuitry is configured to:
. The aircraft of, wherein the AC power control circuitry is configured to heat the surface of each wing by supplying an AC current to the electrical connections that flows within the respective wing along a plurality of current paths, each current path extending from one of the electrical connections and following beneath a corresponding one of the coupling strips, wherein the current path is directed by another current flowing in the respective coupling strip.
. The aircraft of, wherein each coupling strip has a multi-layer structure that comprises:
. The aircraft of, wherein the conductive layer comprises copper, and wherein the starboard wing and the port wing each comprise an electrically conductive material having an electrical resistance greater than that of copper.
. The aircraft of, wherein the conductive layer comprises silver, and wherein the starboard wing and the port wing each comprise an electrically conductive material having an electrical resistance greater than that of silver.
. The system of, wherein the conductive layer comprises aluminum, and wherein the starboard wing and the port wing each comprise an electrically conductive material having an electrical resistance greater than that of aluminum.
. The aircraft of, wherein the conductive layer of at least one of the coupling strips is folded one or more times such that segments of the conductive layer lie alongside one another.
. The aircraft of, wherein each of the coupling strips comprise an input end and a termination end,
. The aircraft of, wherein a width of each coupling strip is less than a spacing between coupling strips and a length of each coupling strip is greater than the spacing between coupling strips.
. An aircraft comprising:
Complete technical specification and implementation details from the patent document.
This application is a continuation of and claims priority under 35 U.S.C. § 120 from U.S. application Ser. No. 16/552,045, filed on Aug. 27, 2019, which claims priority to U.S. Patent Application No. 62/723,270, filed on Aug. 27, 2018. The entire contents of each of these priority applications are incorporated herein by reference.
This specification relates to heating systems for conductive materials.
Many conductive surfaces, such as those on cars, aircraft, and satellites encounter cold and icy conditions during every day use. Ice or water accumulation on the conductive surfaces of these structures may result in inefficient or unsafe operating conditions. For example, ice accumulation on aircraft wings may result in lift degradation and increased drag.
Many of these structures do not have heating systems, or have heating systems that require using bulky electronics or other equipment. The use of such bulky devices poses a challenge for the industry.
This specification describes technologies for heating a conductive surface. These technologies generally involve using higher frequency alternating electric current (“AC”) signals (e.g., above 1 kHz) to shape current density in a target area of a conductive bulk medium (e.g., conductive material), resulting in Joule heating of the medium.
Joule heating, also known as ohmic heating or resistive heating, is the process by which the passage of an electric current through a conductor produces heat. The amount of heat generated by a conducting medium is based on the amount of current passed through the medium and the electrical resistance of the medium. Consequently, the heating can be controlled (e.g. increased or decreased) by adjusting the current, voltage, resistance, or a combination thereof.
The resistance of a given conductor may be increased by constraining the volume within the conductor in which current can flow and by increasing the length along which the current flows. Implementations of the present disclosure can be configured to produce heating in a bulk medium by manipulating mechanisms for shaping (e.g., constricting, lengthening, etc.) current within a conductive medium (e.g., bulk medium, conductor): for example, by using the skin effect and the proximity effect. Both effects rely on running a high frequency AC current through the conductive medium that is to be heated. The skin effect constrains current flow by taking advantage of the tendency of an alternating electric current to become distributed within a conductor such that the current density increases near the surface of the conductor, and decreases with greater depths in the conductor. The proximity effect can be used to further constrain current flow in the conductor by placing another AC current path near the existing current flowing in the conductor. The proximity effect can also act to lengthen the current path.
For example, implementations of the present disclosure are configured to increase the resistance of a bulk medium along a current path through the medium by constricting the current flow along the path. Consequently, implementations may provide increased heating performance in conductive mediums while at the same time permitting a reduction in the current required to produce the heat. That is, by increasing the effective resistance of a conductive medium along a particular current path, less current may be required to produce Joule heating in the medium than would be required otherwise.
In general, in a first aspect, a system for heating a bulk medium includes two or more electrodes spaced apart from one another and coupled to the bulk medium; and a power control system coupled to the electrodes, the power control system configured to produce an effective resistance of the bulk medium along a current path between the electrodes by shaping a density of the current in the bulk medium, in which the power control system shapes the density of the current within a depth of the bulk medium by tuning a skin-depth of the current along the current path, and in which the power control system shapes the density of the current in a direction across the current path by the power control system by tuning a proximity effect of the current.
A second general aspect can be embodied in a system for heating a bulk medium includes two or more electrodes spaced apart from one another and coupled to the bulk medium; and a power control system coupled to the electrodes, the power control system configured to heat the bulk medium by shaping a density of the current along a current path between the electrodes, thereby, producing an effective resistance along the current path in the bulk medium that is greater than the resistance of the bulk medium to a direct current (DC), in which the power control system shapes the density of the current within a depth of the bulk medium by tuning a skin-depth of the current, and in which the power control system shapes the density of the current in a direction across the current path by the power control system by tuning a proximity effect of the current.
A third general aspect can be embodied in a system includes two or more electrodes configured to be coupled to a bulk medium; and a power control system configured to couple to the electrodes and to heat the bulk medium by shaping a density of current along a current path through the bulk medium between the electrodes, thereby, producing an effective resistance along the current path that is greater than the resistance of the bulk medium to a DC current, in which the power control system shapes the density of the current within a depth of the bulk medium by tuning a skin-depth of the current, and in which the power control system shapes the density of the current in a direction across a portion of the current path by the power control system by tuning a proximity effect of the current.
A fourth general aspect can be embodied in a system includes two or more electrodes spaced apart from one another and coupled to a bulk medium; a power control system coupled to the electrodes and configured to generate an AC current signal along a current path through the bulk medium between the electrodes at a frequency greater than 1 kHz and less than 300 GHz; and a second current path positioned proximate to a surface of the bulk medium and along the current path through the bulk medium.
A fifth general aspect can be embodied in a heating system includes two or more electrodes spaced apart from one another and coupled to a bulk medium; a power control system coupled to the electrodes and configured to generate an AC current signal along a current path through the bulk medium to heat the bulk medium; and an impedance adjusting network (IAN) coupled between the heating control system and the electrodes and configured to adjust an impedance of the heating control system to correspond with an impedance of the bulk medium.
A sixth general aspect can be embodied in a heating system includes two or more electrodes spaced apart from one another and coupled to a bulk medium, each of the two or more electrodes including a material that is at least as electrically conductive as the bulk medium, and being coupled to the bulk medium in a manner that reduces a contact resistance between the electrode and the bulk medium; and a power control system configured to couple to the electrodes, the power control system configured to heat the bulk medium by shaping a density of current along a current path through the bulk medium between the electrodes, thereby, producing an effective resistance along the current path that is greater than the resistance of the bulk medium to a DC current, in which the heating system shapes the density of the current by tuning a skin-depth of the current along the current path.
A seventh general aspect can be embodied in an aircraft de-icing system that includes two or more electrodes spaced apart from one another and coupled to a portion of an aircraft; a power control system coupled to the electrodes and configured to heat the bulk medium by shaping a density of current along a current path through the bulk medium between the electrodes by: generating an AC current signal along a current path through the portion of the aircraft between the electrodes and at a frequency between 1 MHz and 50 MHz, in which the frequency causes the density of the current to be shaped in a first direction by tuning a skin-depth of the current along the current path; and providing a second current path positioned along at least a portion of the current path through the portion of the aircraft and within a proximity of 10 cm of a surface of the portion of the aircraft, in which the proximity of the second current path to the surface of the portion of the aircraft causes the density of the current to be shaped in a second, different, direction by tuning a proximity effect of the current along the portion of the current path.
An eighth general aspect can be embodied in a system for heating an exterior surface of a bulk medium. The system includes two or more coupling strips spaced apart from one another and attached to the bulk medium. Each of the coupling strips has a multi-layer structure extending along a surface of the bulk medium that forms, in combination with the bulk medium, an electrical transmission line. The multi-layer structure includes a first dielectric layer over the bulk medium, a conductive layer over the first dielectric layer, a second dielectric layer over the conductive layer, and a conductive shielding layer over the second dielectric layer. A power control system is coupled to the conductive layer of each of the coupling strips and to the bulk medium. The power control system is configured to heat the surface of the bulk medium by providing electrical current to the coupling strips. In various implementations, the bulk medium can be an aircraft skin, a wind turbine blade, a roof of a building, or railroad tracks.
A ninth general aspect can be embodied in a system for heating an exterior of a structure, where the structure is made from a non-conductive material. The structure includes a bulk conductive material embedded therein. The system includes two or more coupling strips spaced apart from one another and attached to the structure. Each of the coupling strips has a multi-layer structure extending along the structure that forms, in combination with the bulk conductive material embedded within the structure, an electrical transmission line. The multi-layer structure includes a conductive layer overlapping the bulk conductive material, and a first dielectric layer between the bulk conductive material and the first conductive layer. The power control system is coupled to the conductive layer of each of the coupling strips and to the structure The power control system is configured to heat the surface of the structure by providing electrical current to the coupling strips. In various implementations, the structure can be an aircraft skin, a wind turbine blade, a roof of a building, or railroad tracks.
A tenth general aspect can be embodied in a method of installing a bulk medium heating system. The method includes obtaining coupling strips, where each coupling strip comprises a multi-layer structure that includes a first dielectric layer, a conductive layer overlapping the first dielectric layer, a conducive shielding layer overlapping the conductive layer, and a second dielectric layer between the conductive layer and the conducive shielding layer. The method includes attaching each of the coupling strips to a surface of an bulk medium and spaced apart from one another with the first dielectric layer of each coupling strip positioned between the bulk medium and the conductive layer. The method includes coupling the conductive layer of each of the coupling strips to a power control system that is configured to provide electrical current to the coupling strips. In various implementations, the bulk medium comprises an aircraft skin, a wind turbine blade, a roof of a building, or railroad tracks.
The subject matter described in this specification may be implemented so as to realize one or more of the following advantages. A lighter, less bulky electrical system may be used to heat a conductor. In addition, heating may be localized to the target area, and not overheat the heating system circuitry. The heating system may be more efficient, for example, by generating heat directly in a bulk medium (e.g., aircraft wing) itself rather than generating heat in a heating element or heating layer attached to the bulk medium. The system may also use less current and voltage for heating, potentially improving safety and reliability. In some implementations, component stress may also be reduced. The system may be easier, faster, or cheaper to install or retrofit. The system may be cheaper or easier to maintain. The system may be non-invasive when retrofitted into existing systems. The system may be faster at de-icing.
The details of one or more implementations of the subject matter of this specification are set forth in the accompanying drawings and the description below. Other features, aspects, and advantages of the subject matter will become apparent from the description, the drawings, and the claims.
Like reference numbers and designations in the various drawings indicate like elements.
The heating system of the present specification uses AC currents in order to increase the effective electrical resistance of conductive materials (e.g., aluminum, carbon fiber composites) in order to more easily heat them. In general, the heat generated in the conductive material can be used to melt ice that has formed on the surface of the conductive material. The heat can also be used to keep conductive materials at an elevated temperature in order to prevent vapor deposition on the surface, or to keep water from freezing on the surface, as well as to prevent freezing precipitation (e.g., snow, ice pellets, fog, freezing rain) from accumulating on the surface. For example, the heat generated in the conductive material may conduct (e.g., spread out) throughout the conductive material. In addition, the heat generated may cause convection across the interface between the conductive material and the any liquid on the surface in order to, for example, heat the liquid and prevent it from freezing.
Alternating currents can be utilized to induce a number of electromagnetic effects that increase the effective resistance of a conductive material, thereby facilitating heat generation using Joule heating in the conductive material. Such effects include the skin effect, the proximity effect, induction, eddy currents, hysteresis losses, and dielectric losses. With the skin effect, if the frequency of the current in a conductor is set to a sufficiently high value, the majority of the current will pass through a skin depth of the conductive material that is significantly less than the conductive material's geometric thickness. In addition, specific device geometries can be used to generate the proximity effect within the conductive material, which will further constrain the width of the current density, thereby, further increasing the effective resistance along a current path within the conductive material. Taken together, these two effects can be used to increase the electrical resistance of the conductive material and result in Joule heating.
For example, Joule heating generally refers to heat produced by passing an electric current through a conductor. The heat generated in a given current carrying conductor is proportional to the resistance of the material times the root mean square of the amplitude of the current squared:P∝IR
Heat output from a heating element is generally increased by increasing the current passed through a conductor and by having relatively higher resistance heating elements. However, implementations of the present disclosure generate Joule heating by leveraging particular electromagnetic phenomena (e.g., skin effect and proximity effect) to constrict the current density of a localized current within a bulk medium. This constriction in current density produces an increased effective resistance along the current's path within the bulk medium. While specific effects may vary in different materials and with different geometries, the effective resistance for a given length along the current path through a bulk medium can generally be represented as:
where ρ represents the resistivity of the material through which the current flows, l represents the length of the current path, and Arepresents the constricted cross-sectional area of the current density. Implementations of the present disclosure use the electromagnetic phenomena to reduce Ato an area less than the cross-section of the bulk medium along the current's path, thereby, increasing the effective resistance of the bulk medium above that of the bulk medium to a DC current.
Some implementations of the present disclosure can use these electromagnetic phenomena to increase the length of a current path through the bulk medium. For example, as described in reference tobelow, techniques described herein can be used to “steer” the current path along a non-direct route (e.g., a serpentine path) between two electrodes attached to the bulk medium. The non-direct route may create a current path that has an effective length (I) that is longer than a substantially straight path that would generally be produced by passing a current between the two electrodes in the absence of electromagnetic effects such as the proximity effect, for example. Thus, systems described herein may increase the current path length l to an effective length (I) that is longer than a direct path that the current would take in the absence of the various systems and conductor arrangements described herein. Accordingly, such implementations may increase the effective resistance (Reff) by both constricting the effective cross-sectional area (A) of a current flowing through a bulk medium and also increasing the effective length (I) that the current traverses through the bulk medium, thereby, further increasing the effective resistance of the bulk medium above that of the bulk medium to a DC current. In such implementations, the effective resistance can be generally represented as:
Through the use of such techniques, implementations of the present disclosure can produce high localized resistances in conductive bulk materials (e.g., aluminum, copper, steel, and alloys thereof).
Skin effect, as used herein, generally refers to the tendency of an alternating electric current to be unevenly distributed in a conductor, such that the current density is larger near the surface of the conductor and decreases as distance to the conductor's surface increases. The intensity of the skin effect increases with the frequency of the current and with the conductivity of the material that carries the current. Some implementations of the present disclosure may tune the skin effect to cause the electric current to flow more at the outer surface of the conductor (e.g., “skin depth”) at higher AC frequencies.
In general, the skin effect in a conductor can be represented by the following formula:
In the case of a rectangular, infinitely long and wide plate on which a surface current flows, the skin effect can be represented by the following formula:
For example, the chart shown in, and discussed in more detail below, illustrates an example of current density constriction within the depth of the material (e.g., skin depth) that is caused by the skin effect.
Proximity effect, as used herein, generally refers to the effect of AC current flowing in a first current path (e.g., conductor) on the current density of an AC current flowing in a second, nearby, current path. For example, as shown inand described in more detail below, the AC current in the first current path causes the density of the AC current in the second current path to “crowd” or constrict around the first current path. In implementations of the present disclosure, for example, the density of a current passing through a bulk medium is “pulled” towards another conductor carrying an AC current when the conductor is placed proximate to current passing through the bulk medium. The degree and direction of current density constriction (e.g., crowding) caused by the proximity effect is dependent on several variables including, for example, the distance between two or more AC current paths, the direction of current travel in the individual current paths relative to each other, the frequencies of the AC currents in the current paths, and the magnitude of the individual currents in the current paths.
For clarity, the heating system of the present disclosure will be described in reference to the example context of a de-icing and anti-icing system for an external surface of an airplane. However, the heating system of the present disclosure can be used in other contexts including, but not limited to, heating the surfaces of other aircraft, drones, wind turbines, units in cryogenic operations, heat pumps, cars, radio towers, railroad tracks, manned or unmanned military vehicles, roofs, or heating other conductive surfaces that may benefit from control of ice or water formation. The heating system can be used for de-icing or anti-icing. In some implementations, the heating system can be used to heat less conductive materials by, for example, applying a conductive layer over or inside a non-conductive material. Such implementations can be used to heat surfaces of roadways (e.g., driveways), building materials, roofs, floors or other low- or non-conductive materials.
De-icing, as used herein, generally refers to removal of snow, ice or frost (collectively referred to as “ice”) from a surface. In some implementations, the heating system can melt only a portion of existing ice on a conductive surface. The ice would then be removed from the surface (e.g., by slipping off the surface once the melting process has started and the ice-surface bond has been broken).
Anti-icing, as used herein, generally refers to the prevention of the formation of or the adherence of snow, ice or frost (collectively referred to as “ice”) to a surface. In some implementations, the heating system maintains the surface temperature high enough to prevent ice from forming on the surface and prevent ice accumulation or formation (e.g., from freezing precipitations such as snow, frost, ice pellets, freezing rain, etc.).
shows a block diagram of an example heating systemfor heating a bulk medium. Heating systemincludes power control systemcoupled to electrodesand. Electrodesandare coupled to a target area of the bulk medium(e.g., part of an aircraft wing). The power control systemgenerates alternating current (AC current) (e.g., of frequencies 1 kHz or higher) across a closed circuit through wire (or path or cable), bulk medium, and finally wire (or return path). The direction of currentthrough the wires is indicated by a dashed arrow.
In some implementations, the heating systemcan include, but is not limited to, power control system, electrodesand, and specialized cables (e.g., wiresand). In some implementations, the heating system is configured to be coupled to electrodesand. In some implementations, the heating system is configured to be coupled to specialized cables (e.g.,or). In some implementations, power control systemcan include, but is not limited to, a signal generating unit, power source, a signal transforming unit, an impedance adjusting network, a control unit, and sensors, with specific configurations described in more detail below. As detailed below, in some implementations, the impedance adjusting network is an impedance matching network.
In some implementations, electrodesandare contact electrodes. For example, electrodesandare physically connected to the bulk mediumto conduct electrical current from the power control systemto the bulk medium. In some implementations, electrodesandcan be coupled to the bulk mediumbut electrically insulated from the bulk medium. For example, in such implementations, electrodesandcan be the input and output of an induction coil that is positioned proximate to the bulk mediumto magnetically induce a current in the bulk medium.
Power control systemcan supply current at a sufficiently high frequency (e.g., above 1 kHz) to constrict current flow in the z-direction between electrodesandby tuning the skin effect, resulting in higher resistance of bulk medium. For example, the power control systemcan provide AC current at a frequency between 1 kHz and 300 GHz. In some implementations, the current frequency is between 10 kHz and 30 GHz. In some implementations, the current frequency is between 100 kHz and 450 MHz. In some implementations, the current frequency is in a range of 1 MHz-50 MHz, 100 MHz-150 MHz, 200 MHz-300 MHz, 400 MHz-500 MHz, or 800 MHz-1 GHz.
In some implementations, the return pathis arranged in close proximity to the surface of the bulk medium. The proximity of the return pathto the surface of the bulk medium can be used to tune the proximity effect of the current flowing between electrodesandand, thereby, further constrict the current and increase the heating within the bulk medium. In order to harness the proximity effect to shape the current flowing between electrodesandit is not necessary to use the return current pathfrom the heating system circuit itself. In some implementations, another current path(e.g., from different circuit) can be placed in close proximity (e.g., distance) to the bulk medium. For example, when the distanceorof current pathorfrom bulk mediumis sufficiently small, the proximity effect can be used to further constrain current through the bulk medium.
For example, the distance(or) between the bulk medium and path(or) can be less than 1 m, or less than 50 cm, or less than 10 cm to produce a proximity effect. If closer distances are possible, with due consideration for design constraints (e.g., with an airplane wing as bulk medium, where the rib or spar of airplane is not in the way of the return path/), distance(or) can be less than 25 cm or less than 10 cm.
The bulk mediumcan include materials such as, but not limited to, aluminum, metal alloys, carbon fiber composites, copper, silver, titanium, or steel. For example, the bulk medium can be any part of an aircraft airframe (e.g., outer-most shell or surface of airplane, also known as airplane's “skin”) such as fuselage, wings, undercarriage, empennage, etc.
The electrodes (and) can include materials such as, but not limited to, aluminum, silver, copper, alloys thereof, or other conductive materials. In some implementations, the electrode material is at least as electrically conductive as bulk medium. In some implementations, electrodesandcan be arranged in arrays of electrodes. The electrodes may be coupled to the bulk medium in a variety of ways, e.g., to the top or bottom surface of the medium, or embedded inside the medium.
Heating systemis configured to produce an effective resistance through bulk mediumby shaping the density of the current through the medium. In other words, for airplane applications, the existing airframe of the airplane will be used as part of the electrical circuit of the heating system. Heating systemshapes the density of the current by tuning the skin effect, the proximity effect, or a combination thereof to increase the effective resistance of the bulk mediumalong a current path between the electrodesand. In some cases, the proximity effect is also leveraged to direct the current path, for example as seen inin order to heat desired sections of the bulk medium. A desired heat section of the bulk medium may be referred to as a “target heating location” or “target location.”
In some implementations, an alternating current of frequency 1 kHz or higher can be passed directly through an airframe of the plane. As a result, Joule heating will occur in the portion of the airframe near the surface that has current passing through it. Additionally, heat produced from the current will be spread by conduction throughout the bulk medium.
Referring to, heating systemshapes the current density through medium target areaby utilizing the skin effect. As in, an AC current (in direction) is applied across electrodesandthrough a target area of bulk medium.is a schematic diagram illustrating the profile (e.g., side view) of current densitythrough bulk mediumtarget area without the skin effect (e.g., with current frequencies below 1 kHz). The current is running in the y-direction (), with the majority of the current flowing within the volume of mediumindicated by the arrows. For example, the current has a depthof about 2 mm, for example, nearly the entire thickness of the bulk medium. As such,illustrates an operation of systemwith little or no shaping of the current density by the skin effect.
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March 31, 2026
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